Design Method of Cardioid Pattern by CMA

Kazuki Kamiyama, Bakar Rohani and Hiroyuki Arai Graduate School of Engineering, Yokohama National University

79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan.

E-mail : kamiyama-kazuki-tf@ynu.jp, rohani-bakar-ng@ynu.ac.jp, arai-hiroyuki-vk@ynu.ac.jp

Abstract –This paper presents a design method of 2-element

monopole with cardioid pattern using Characteristic Mode

Analysis (CMA). First, the inductance L was determined from S11, and then the cardioid pattern was reproduced by the MS value. The final structure of the antenna based on the design

method confirms that the cardioid pattern has F/B ratio of more than 20 dBi for element-spacing of 0.1λ and the directivity gain of around 5 dBi has been achieved. Moreover, it is possible

to reproduce the cardioid pattern by removing L due to the neutralization effect from the size of inductance.

Index Terms — Characteristic mode analysis, modal

significance, cardioid pattern, neutralization effect

1. Introduction

Recent development in mobile wireless communication

system shows an increasing in antenna design with smaller

size and applies less power utilization but at the same time

capable of delivering high capacity content. For smart

devices design such as wearable terminal, miniaturization

technique is implemented in most antenna design. Therefore,

this time we propose an antenna with cardioid pattern that

meets the above requirements. In [1], cardioid pattern was

obtained when 2-element antenna with quarter wavelength

are fed by 90° phase difference in spacing. In this paper, we

propose a 2-element monopole design method showing

cardioid pattern by Characteristic Mode Analysis (CMA)

technique, [2]-[5]. As shown in TABLE I, the optimization

of the antenna parameters is carried out by analyzing the

characteristic mode (CM) characteristic instead of the usual

try and error parameter adjustment using FEKO simulation

software [6].

TABLE I. Antenna parameters of 2-element monopole (d =

0.1λ).

l/λ w

[mm]

h

[mm]

L

[nH]

Main

[dBi]

F/B

[dBi]

0.239 (Sim.) 200

16.4 300

4.96 28.3

0.243 (Exp.) 17.5 4.06 10.5

2. Directivity synthesis by complex amplitude ratio

Fig. 1(a) shows the structure of a 2-element monopole. In

this study, 2-element monopole was designed in simulator,

setting frequency, f at 1 GHz, and exciting single port where

coupling current was performed. L was applied as a

decoupling circuit for input matching. In CMA, current, J on

the surface can be expressed by a linear combination of a

plurality of orthogonal eigen current modes, Jn and its

weighting coefficient, un as shown in (1)

𝐽 =∑ 𝑢𝑛𝐽𝑛𝑁

𝑛=1 (1)

As a result of the analysis, the weight, un of the two modes

(Pattern 1 and Pattern 2) shown in Fig. 1(b) is high at f = 1

GHz and contributes greatly to the directivity formation.

From the figure, currents of anti-phases in Pattern 1 and in-

phase in Pattern 2 flow as shown in current distribution

respectively, and each have a pattern of eight and omni-

directionality.

(a)

(b)

Fig. 1. (a) structure of 2-element monopole, and

(b) current distribution.

In (2), the least squares (LS) method is used for directivity

synthesis of two modes. The method is applied to total

directivity, yi and mode directivity, xi for the angle, φ and LS

solution, α and the regression line, f(x) are obtained. Then,

the amplitude ratio of f(x) that inclination, β is 1 is obtained.

Here, let f(x) be the sum of the ratio of two-mode

directivities which f(x) and yi are normalized. Fig. 2 shows

the transition of radiation pattern synthesis of Eφ with respect

to ground plane width, w. An appropriate complex ratio of

two modes forms a cardioid pattern.

{

𝛼 = 𝑚𝑖𝑛 ‖∑ (𝑦𝑖– 𝑓(𝑥𝑖))𝑛

𝑖=1‖2

𝑓(𝑥) =∑ 𝑓(𝑥𝑘)𝑛

𝑘=1= 𝛽 ∙∑ 𝑥𝑘

𝑛

𝑘=1

(2)

[WeD2-4] 2018 International Symposium on Antennas and Propagation (ISAP 2018)October 23~26, 2018 / Paradise Hotel Busan, Busan, Korea

115

Fig. 2. Directivity synthesis by mode amplitude ratio.

3. Design of cardioid pattern by mode excitation ratio

by MS value

The cardioid pattern can be reproduced by complex

amplitude ratio of 2 modes. In this section, the antenna is

designed to obtain the optimum amplitude ratio. First, the

inductance, L that minimizes S11 is determined as shown in

Fig. 3(a). As a result of the adjustment, S11 became minimum

at L = 0.01 [nH]. Next, using Modal Significance (MS) value

that indicates the degree of mode resonance, the antenna

parameters are adjusted to obtain the amplitude ratio. Fig. 3

shows the characteristics of each parameter. The degree of

resonance of the entire mode changes by the ground plane, w

and that of Mode 1 (Pattern 1) and Mode 5 (Pattern 2)

changes by antenna element length, l. On the other hand,

degree of mode resonance by the bridge height, h is almost

constant, so there is no contribution to resonance.

(a) (b)

(c) (d)

Fig. 3. (a) S11 for inductance, L, MS value characteristic for

(b) ground plane width, w, (c) bridge height, h and,

(d) element length, l.

As a result, the parameters were adjusted to increase F/B

ratio. Fig. 4 shows the optimum MS value ratio of the two

modes at each element-spacing and the directivity obtained

by it. The parameters in TABLE II reproduced the cardioid

pattern with the maximum gain of 4.77 dBi and F/B ratio of

22.0 dB at the element-spacing, d = 0.1λ. At this time, the

same result was obtained by removing L due to very small

value that can be ignored and inserting a short line. This is

because the neutralization effect reduces the mutual coupling

and becomes a decoupling circuit.[7]

Fig. 4. Cardioid pattern of different element-spacing, d.

TABLE II. Optimum antenna parameters of 2-element

monopole (with short line).

d/λ l/λ w

[mm]

h

[mm]

Main

[dBi]

F/B

[dBi]

0.1 0.239

200 1.5

4.77 22.0

0.075 0.241 4.96 14.5

0.05 0.244 5.06 10.1

4. Conclusion

In this paper, a design method of cardioid pattern synthesis

by CMA is shown by simulation for 2-element monopole.

Based on a certain ground plane width, w, an ideal cardioid

pattern can be obtained by adjusting the antenna element

length, l in order to achieve an ideal mode resonance ratio.

References

[1] Takashi Ohira, “Espar Antennas: Basic Theory and System Applications”, IEICE Vo.87, No.12, Dec.2004.

[2] M. C. Fabres, E. A. Daviu, A. V. Nogueira and M. F. Bataller, “The

theory of characteristic modes revisited: a contribution to the design of antennas for modern applications,” IEEE Antennas and

Propagation Magazine, 2007, vol. 49, no. 5, pp. 52-68.

[3] Akira Noguchi and Hiroyuki Arai, “3-Element super-directive endfire array with decoupling network” International Symposium on

Antennas and Propagation (ISAP), 2014, Kaohsiung, pp. 455-456.

[4] Bakar Rohani, Kazuki Kamiyama, and Hiroyuki Arai “Cardioid Type Pattern Optimization Using Characteristic Mode Analysis,”

European Association on Antennas and Propagation (EuCAP), 2018,

London, CS08.1 pp. 1-4. [5] Shen Wang and Hiroyuki Arai, “Characteristic Modes Analysis on

Neutralizing Effect of Shorted Line for Two Adjacent PIFA

Elements,” International Workshop on Antenna Technology (iWAT) , 2014, Sydney, pp. 89-90.

[6] FEKO: EM Simulation Software. [https://www.feko.info/].

[7] Aliou Diallo, Cyril Luxey, Philippe Le Thuc, Robert Staraj, and Georges Kossiavas “Study and Reduction of the Mutual Coupling

Between Two Mobile Phone PIFAs Operating in the DCS1800 and

UMTS Bands,” IEEE Trans. Antennas Propagat. Soc., 2006, vol.54, no.11, pp.3063–3074.

2018 International Symposium on Antennas and Propagation (ISAP 2018)October 23~26, 2018 / Paradise Hotel Busan, Busan, Korea

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